Ornstein–Uhlenbeck process

GPTKB entity

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Predicate	Object
gptkbp:instanceOf	gptkb:stochastic_process
gptkbp:application	modeling commodity prices modeling interest rates modeling neuronal activity
gptkbp:describes	velocity of a Brownian particle with friction
gptkbp:governingEquation	dX_t = θ(μ - X_t)dt + σdW_t
gptkbp:hasSpecialCase	gptkb:Langevin_equation
https://www.w3.org/2000/01/rdf-schema#label	Ornstein–Uhlenbeck process
gptkbp:introducedIn	1930
gptkbp:limitingDistribution	gptkb:normal_distribution
gptkbp:namedAfter	gptkb:George_Eugene_Uhlenbeck gptkb:Leonard_Ornstein
gptkbp:parameter	W_t (Wiener process) θ (rate of mean reversion) μ (long-term mean) σ (volatility)
gptkbp:relatedTo	gptkb:Wiener_process Brownian motion
gptkbp:solvedBy	X_t = μ + (X_0 - μ)e^{-θt} + σ∫₀^t e^{-θ(t-s)}dW_s
gptkbp:stationaryDistribution	gptkb:Gaussian_distribution
gptkbp:type	gptkb:Gaussian_process Markov chain mean-reverting process stationary process
gptkbp:usedIn	biology finance physics
gptkbp:bfsParent	gptkb:George_Uhlenbeck
gptkbp:bfsLayer	4